After months of Donald Trump's warnings that the presidential election will be rigged against him, Republican officials are joining Democrats in denouncing the claims.

South Carolina senator Lindsay Graham, Ohio Secretary of State Jon Husted, and former Missouri senator Kit Bond are among the GOP leaders who have spoken out against Mr. Trump's warnings of election rigging, calling for the nominee to either produce evidence of widespread voter fraud or to stop talking about it.

Trump's claims come in the midst of a nationwide debate over voter identification laws, which Republican lawmakers have long pushed as a way to combat what they see as the threat of voter fraud. But Trump's warnings and calls for supporters to monitor the polls on election day in "certain areas" have raised concerns about voter intimidation and questions regarding the future of democracy in the United States.

Now, some Republican leaders are speaking up against Trump's rhetoric, a seemingly contradictory stance that observers say is likely driven by a combination of self-interest and a worry that widespread distrust in the democratic process could undermine the integrity of future elections.

"I don't think it's good for democracy to have a major candidate for president doubt the outcome," Senator Graham, who ended his own 2016 presidential run in December, told CNN last week, adding, "I believe that the country will survive long after I'm gone but the country really is a process and the election process I think we need to respect it rather than create doubt about it. Americans have enough to worry about already. Let's don't suggest the election's rigged."

Widespread acceptance of vote rigging as the cause of a potential Trump loss could set a dangerous precedent, says Jimmy Camp, a former Republican political consultant, now independent, who left the party because of Trump’s nomination.

"If Donald Trump says that Hillary Clinton wins because she cheated or because the process is rigged, then anyone who loses can make that claim," Mr. Camp tells The Christian Science Monitor in a phone interview.

Republicans such as Senator Graham have cited concern for the future of the election process as a primary reason for their disapproval. But Trump is not the first Republican presidential candidate to make accusations of widespread election rigging, points out Lorraine Minnite, professor of political science at Rutgers University-Camden: John McCain, in a 2008 presidential debate against President Obama, said that the community organizing group ACORN "is now on the verge of maybe perpetrating one of the greatest frauds in voter history in this country, maybe destroying the fabric of democracy."

Senator McCain didn't receive as much backlash from Republican leaders for his comments, Professor Minnite adds, suggesting that the motivation of Graham and others speaking out against Trump may be more self-serving than born out of concern for the democratic process.

Real Clear Politics’ aggregate of national polls on Wednesday shows Trump pulling in an average of 41.8 percent, compared to Mrs. Clinton’s 48 percent. As November draws closer, Republicans "are worried that Trump's likely defeat will bring down other Republicans, and they are distancing themselves from him," Minnite says.

At the same time, politicians are driven by a need to appeal to voters' beliefs, particularly when it comes to issues such as voter fraud, Camp points out. A recent Washington Post-ABC poll found that 46 percent of registered voters – and more than two-thirds of Trump supporters – believe that voter fraud, defined as multiple votes being cast by a single person or an ineligible person casting a ballot, occurs very or somewhat often, despite evidence to the contrary.

Experts attribute the high percentages not to Trump, but to a history of Republican lawmakers campaigning against voter fraud to pass voter identification laws.

"Republicans have been for a while using claims of vote fraud as rationale for passing voter ID laws," says Michael McDonald, professor of political science at the University of Florida, in a phone interview with the Monitor. "And so that Trump would be parroting what other Republicans have been saying for a long time, and the rationale for them to pass these laws, is not surprising at all."

Now, as Republican lawmakers speak out against Trump's rigged election warnings, some have attempted to maintain a stance against voter fraud or in support of voter identification laws while denouncing the extreme nature of Trump's claims.

"I for a long time have been critical of people in both political parties who have tried to undermine public confidence in our election, rather by saying the election is going to be rigged or suggesting that people are being disenfranchised," said Ohio Secretary of State Jon Husted in a statement last week.

Lanhee Chen, a former Mitt Romney 2012 policy adviser, told Politico that while he believes that some degree of voter fraud takes place around the country, he doesn't feel the practice is widespread enough to warrant such attention from a presidential candidate.

"Ultimately, is it enough to compromise an election? Probably not," Mr. Chen said. "Credible Republicans have to be a note of sobriety, and we do have to respect the outcome of the election."